Find the area of the quadrilateral whose vertices are

(6, 9), (7, 4), (4,2) and (3,7)

When the vertices of a quadrilateral is given then its area is given by {(x₁–x₃)(y₂–y₄) – (x₂–x₄)(y₁–y₃)}

We must take all the vertices in counter clock wise direction otherwise it will give solution in negative.

So, from the figure we assume that

A (x₁, y₁) = (7,4)

B (x₂, y₂) = (6, 9)

C (x₃, y₃) = (3, 7)

D (x₄, y₄) = (4, 2)

The area of the quadrilateral is {(x₁–x₃)(y₂–y₄) – (x₂–x₄)(y₁–y₃)}

= {(7–3)(9–2) – (6–4)(4–7)}

= {28–(–6)} = 17 Sq. units